MPL estimation of a proportional hazards mixture cure model with partly-interval censoring

Proportional hazards mixture cure models are an important tool in survival analysis because they account for the presence of a sub-population who will never experience the event of interest. Much previous research in this area has been limited in scope to right censored data and has not offered a smooth estimate of the baseline hazard function. This thesis considers a maximum penalised likelihood (MPL) estimation of a proportional hazards mixture cure model for partly-interval censored survival data. The MPL method simultaneously estimates all model parameters, including a smooth Mspline approximation to the baseline hazard function. The non-negativity constraint on the baseline hazard function is guaranteed through the use of a multiplicative-iterative algorithm. Asymptotic properties are presented to allow for large sample inference on all parameters, including regression parameters and survival quantities. The results of two simulation studies are presented to demonstrate the method's performance, including a comparison to an existing method. A newly developed package for implementing the model in R is outlined and an example of its use is demonstrated with data from a melanoma study.